Heterogeneous catalysis is of paramount importance in many areas of gas conversion and processing in chemical engineering industries. In porous pellets, the catalytic reactions may be affected by diffusional limitations such that the global rate can be different from the intrinsic reaction rate. In the literature, a number of multicomponent diffusion flux closures have been applied to characterize the diffusion process within different units in chemical process plants. The main purpose of this paper is to outline the derivation of the different diffusion flux models: the rigorous Maxwell-Stefan and dusty gas models, and the simpler Wilke and Wilke-Bosanquet models. Usually the diffusion fluxes are derived and presented with respect to the molar average velocity definition. In this study, also the diffusion flux closures with respect to the mass average velocity definition is outlined. Thus, if the temperature equation and the momentum equation are used in the pellet model, a consistently closed set of pellet equations is obtained on mass basis holding only the mass average velocity. On the other hand, for the closed set of pellet equations on molar basis, the component balances hold the molar averaged velocity whereas the temperature and momentum equations hold the mass average velocity due to the physical laws applied deriving these fundamental balances. Nevertheless, the Maxwell-Stefan and dusty gas models are manipulated and put on the convenient Fickian form. The second purpose of this article is the evaluation of the diffusion flux closures derived. For this purpose, a transient model is developed to describe the evolution of the species composition, pressure, velocity, temperature, total concentration, and fluxes within a spherical pellet. The catalyst problem has been simulated for the methanol dehydration process producing dimethyl ether (DME), with computed efficiency factor values in the range 0.06-0.6 for pellet pore diameters of 0.1-100 nm. Identical results are expected for the mole and mass based pellet equations. However, deviations are obtained in the component fractions comparing the mass and mole based pellet model formulations where the mass fluxes were described according to the Wilke and Wilke-Bosanquet models. On the other hand, the rigorous Maxwell-Stefan and dusty gas models gave identical results.